Millimeter wave beaconing with directional antennas

ABSTRACT

A wireless device comprises a code-assignment module configured for assigning Golay codes to be used for spreading, a spreading module configured for spreading data with the Golay codes to produce a signal, wherein the Golay codes are randomly used to spread the data, and a transmitter configured for transmitting the signal. The wireless device may transmit a first beacon signal via a set of quasi-omni beam patterns, and a second beacon signal via a set directional beam patterns. The first beacon signal has a first transmission rate that is higher than the second beacon signal&#39;s the transmission rate. Extended Golay codes having zero periodic cross-correlation may be generated from a Golay code and a set of short sequences. A data block transmitted by the wireless device may comprise Golay codes and data portions, wherein every data portion is between two Golay codes and every Golay code is between two data portions.

CLAIM OF PRIORITY UNDER 35 U.S.C. §119

The present Application for Patent claims priority to ProvisionalApplication No. 60/998,278 filed Oct. 10, 2007, and assigned to theassignee hereof and hereby expressly incorporated by reference herein.

BACKGROUND

I. Field of the Invention

The invention relates generally to generating spread-spectrum coding,and particularly to generating and processing Golay codes.

II. Description of the Related Art

In one aspect of the related art, a Physical Layer supporting bothsingle carrier and Orthogonal Frequency Division Multiplexing (OFDM)modulation may be used for millimeter wave (e.g., 60 GHz)communications. For example, aspects of the invention may be configuredfor millimeter wave communications in the 57 GHz-66 GHz spectrum (e.g.,57 GHz-64 GHz in the United States, and 59 GHz-66 GHz in Japan).

Both OFDM and single-carrier modes further include a single-carriercommon mode. The common mode is a base-rate mode employed by both OFDMand single-carrier transceivers to facilitate co-existence andinteroperability between different devices and different networks. Thecommon mode may be employed for beaconing, transmitting controlinformation, and as a base rate for data packets. Common-mode data isspread by Golay codes and employs π/2-BPSK modulation.

A single-carrier transceiver in an IEEE802.15.3c network typicallyemploys at least one Golay-code generator to provide Golay codes to allof the fields of a transmitted data frame and to performmatched-filtering of a received Golay-coded signal. Complementary codes,first introduced by Golay, are sets of finite sequences of equal lengthsuch that the number of pairs of identical elements with any givenseparation in one sequence is equal to the number of pairs of unlikeelements having the same separation in the other sequences. S. Z.Budisin, “Efficient pulse compressor for Golay complementary sequences,”Electronic Letters, 27, no. 3, pp. 219-220, 31 Jan. 1991, which ishereby incorporated by reference, shows a transmitter for generatingGolay complementary codes as well as a Golay matched filter.

SUMMARY

Aspects disclosed herein may be advantageous to systems employingmillimeter-wave WPANs, such as defined by the IEEE802.15.3c protocol.However, the invention is not intended to be limited to such systems, asother applications may benefit from similar advantages.

In one aspect of the invention, a transmitter is configured forassigning Golay codes to be used for spreading, spreading data with theGolay codes to produce a signal, wherein the Golay codes are randomlyused to spread the data, and transmitting the signal.

In another aspect of the invention, a transmitter is configured fortransmitting a first beacon signal via a set of quasi-omni beam patternsand a second beacon signal via a set of directional beam patterns,wherein a first rate associated with the transmission of the firstbeacon signal is higher than a second rate associated with thetransmission of the second beacon signal.

In another aspect, a transmitter or a receiver generates a preambleusing an extended Golay code. The extended Golay code is selected from aset of extended Golay codes having zero periodic cross-correlation,which are generated from a Golay code and a set of short sequences.

In yet another aspect, a transmitter generates a first data blockcomprising Golay codes and data portions, wherein every data portion isbetween two Golay codes and every Golay code is between two dataportions.

Although particular aspects are described herein, many variations andpermutations of these aspects fall within the scope of the invention.Whereas some benefits and advantages of the preferred aspects arementioned, the scope of the invention is not intended to be limited toparticular benefits, uses, or objectives. Rather, aspects of theinvention are intended to be broadly applicable to different wirelesstechnologies, system configurations, networks, and transmissionprotocols, some of which are illustrated by way of example in thefigures and in the following Detailed Description. The detaileddescription and drawings are merely illustrative of the invention ratherthan limiting, the scope of the invention being defined by the appendedclaims and equivalents thereof.

BRIEF DESCRIPTION OF THE DRAWINGS

Aspects according to the invention are understood with reference to thefollowing figures.

FIG. 1 is a diagram of a frame structure for a packet in a common-modecommunication signal in accordance with a sample aspect of theinvention.

FIG. 2 illustrates communication links between two pairs of wirelesstransceivers.

FIG. 3 illustrates a method for implementing wireless communications inaccordance with a sample aspect of the invention.

FIG. 4 is a block diagram of an apparatus configured for communicatingin a millimeter-wave system.

FIG. 5 is a block diagram of a Golay-code generator that may be employedin some aspects of the invention.

FIG. 6 illustrates software components residing on a computer-readablememory and configured in accordance with a sample aspect of theinvention.

FIG. 7 is a flow diagram for a communication method in accordance with asample aspect of the invention.

FIG. 8 is a block diagram of a sample apparatus configured in accordancewith a sample aspect of the invention.

FIG. 9 illustrates software components residing on a computer-readablememory and configured in accordance with a sample aspect of theinvention.

FIG. 10 is a flow diagram depicting a sample method for generating apreamble with a set of extended Golay codes havinglow-cross-correlation.

FIG. 11 is a block diagram of a sample apparatus configured forgenerating a preamble.

FIG. 12 illustrates software components residing on a computer-readablememory and configured in accordance with a sample aspect of theinvention.

FIG. 13 is a flow diagram depicting a sample method for generating acommunication signal for transmission.

FIG. 14 is a block diagram of an apparatus configured for generating asignal in accordance with a sample aspect of the invention.

FIG. 15 shows a sample format of a sub-slot structure.

FIG. 16 shows a sample format of a sub-block structure in which thesub-slot length is reduced by the channel delay.

FIG. 17 illustrates a sample block structure in which each of the firstN/2 sub-slots in a first block employs a first complementary Golay codeas a prefix.

FIG. 18 illustrates a sub-block structure in accordance with a sampleaspect of the invention configured to reduce the presence of spectrallines due to periodic structure in the frame.

FIG. 19 illustrates a sub-block structure that may be employed invarious aspects of the invention.

FIG. 20 illustrates a sub-block structure in which complementary Golaycode a is inserted before even-numbered sub-slots, complementary Golaycode b is inserted before odd-numbered sub-slots, and known pilot chipsor tones are inserted in some or all of the sub-slots.

DETAILED DESCRIPTION

Various aspects of the disclosure are described below. It should beapparent that the teachings herein may be embodied in a wide variety offorms and that any specific structure, function, or both being disclosedherein are merely representative. Based on the teachings herein oneskilled in the art should appreciate that an aspect disclosed herein maybe implemented independently of any other aspects and that two or moreof these aspects may be combined in various ways. For example, anapparatus may be implemented or a method may be practiced using anynumber of the aspects set forth herein. In addition, such an apparatusmay be implemented or such a method may be practiced using otherstructure, functionality, or structure and functionality in addition toor other than one or more of the aspects set forth herein.

In the following description, for the purposes of explanation, numerousspecific details are set forth in order to provide a thoroughunderstanding of the invention. It should be understood, however, thatthe particular aspects shown and described herein are not intended tolimit the invention to any particular form, but rather, the invention isto cover all modifications, equivalents, and alternatives falling withinthe scope of the invention as defined by the claims.

FIG. 1 is a representation of a frame structure for a packet of acommon-mode communication signal in accordance with an aspect of theinvention. The common-mode signal comprises Golay spreading codes withchip-level π/2-BPSK modulation. A preamble may comprise either 8 or 30repetitions of a Golay code having length 128 (e.g., a Golay codedenoted by a₁₂₈). A preamble, as used herein, may further include pilotsignals (not shown). A PLCP header and a PSDU (i.e. data payload)comprise symbols spread with a Golay code pair of length 64 (such asGolay codes a₆₄ and b₆₄). A long preamble (i.e., the preamble comprising30 repetitions of the Golay code) is typically implemented as a defaultpreamble. However, the preamble may be switched to a short preamble(i.e., the preamble comprising 8 repetitions of the Golay code) uponeither an implicit or explicit device request.

Various frame parameters, including, by way of example, but withoutlimitation, the number of Golay-code repetitions and the Golay-codelengths may be adapted in accordance with aspects of the invention. Inone aspect, Golay codes employed in the preamble may be selected fromlength-128 or length-256 Golay codes. Golay codes used for dataspreading may comprise length-64 or length-128 Golay codes.

Aspects of the invention may employ beamforming. For example, FIG. 2illustrates a communication links between two pairs of wirelesstransceivers. A first communication link is provided between a firstwireless transceiver 201 and a second wireless transceiver 202. A secondcommunication link is provided between a third wireless transceiver 211and a fourth wireless transceiver 212.

The first wireless transceiver 201 comprises an antenna array 205, whichis configured for producing a first directional beam pattern 221. Thesecond wireless transceiver 202 comprises a single antenna 206, whichproduces a first substantially omni-directional beam pattern 222. Thethird wireless transceiver 211 comprises an antenna array 215 and isconfigured for producing a second directional beam pattern 231. Thefourth wireless transceiver 204 comprises a single antenna 216, whichproduces a second substantially omni-directional beam pattern 232.

In one aspect, the wireless transceiver 201 employs its direction beampattern 221 to transmit HDTV signals to the second wireless transceiver202. During the transmission, the second wireless transceiver 202 isprimarily in a receiving mode. However, the second wireless transceiver202 may transmit an acknowledgement message (e.g., an ACK or NACK) toacknowledge whether data packets were received correctly. Similarly, thethird wireless transceiver 211 transmits signals via its directionalbeam pattern 215 to the fourth wireless transceiver 204, which alsoreturns acknowledgement messages.

Typically, the pair of communication links employs different frequencychannels to avoid interference. However, since the first and thirdwireless transceiver 201 and 211 employ directional beam patterns, thesame frequency channel may be used for both communication links. Theomni-directional transceivers 202 and 212 use a low-data rate mode, suchas a common mode, to return acknowledgement messages and otherinformation. Interference may occur when one of the omni-directionaltransceivers 202 and 212 transmits an acknowledgement message in thesame frequency band and at the same time the other omni-directionaltransceiver 212 or 202 is in receiving mode. In order to mitigateinterference between the omni-directional transceivers 202 and 212, eachlink may employ a set of Golay codes selected from a plurality ofGolay-code sets having low-cross correlations relative to each other.

In accordance with one aspect of the invention, any of a set of sixGolay complementary code pairs may be employed. For example, a set ofsix Golay code pairs is generated using a delay vector D=[32, 8, 2 16,1, 4] and the following seed vectors:

W ¹=[+1, +1, −j, +j, −j, +1]

W ²=[+1, +1, −1, +1, +j, +j]

W ³ =[−j, +1, +1, −1, −1, +j]

W ⁴ =[+j, +j, −j, −1, +1, +1]

W ⁵=[−1, +1, −1, −1, +j, +j]

W ⁶ =[+j, +1, +1, −1, −1, +j]

The periodic cross correlation between the resulting Golay complementarycodes is less that 16, and the periodic autocorrelation function has azero-correlation zone (i.e., no side lobes) around the main correlationpeak. Since the same delay vector is used to generate all six codes, andonly the seed vector is configurable, code generators configured togenerate different Golay complementary code pairs may share the samehardware configuration. Input signals may include a Dirac impulsesignal. The output comprises the complex-conjugate Golay pair codes inreverse order. For example, the code generator may produce Golaycomplementary code pairs that are mother codes (a^(i) ₆₄, b^(i) ₆₄) oflength 64. The common mode may employ such Golay codes of length 64 or128 for data spreading.

It is well know that Golay codes do not have perfect aperiodicautocorrelation. Rather, the autocorrelation of a Golay code has a mainpeak and some sidelobes having well-defined positions. Consequently,after Golay matched-filtering, the sidelobes appear as channeldistortions resembling paths of a multipath channel. Such false pathscan cause a Rake receiver to mistake the sidelobes as multipathcomponents of a received signal. Thus, aspects of the invention may beconfigured to employ codes that randomize the locations ofautocorrelation sidelobes.

One aspect may employ a set of codes (instead of a single code) for dataspreading. For example, each of a plurality of data symbols may bespread with a different spreading code. Adjacent data symbols may employdifferent spreading codes, or a different spreading code may be employedfor each of a plurality of adjacent symbols. Furthermore, each set ofdevices supporting a different communication link in the same frequencychannel may use a unique set of codes. Each set of codes may be derivedfrom circularly shifted versions of a Golay code.

In one aspect, each circularly shifted Golay code is produced byemploying a constant shift. For example, a second Golay code is producedby circularly shifting a first Golay code by a predetermined amount. Athird Golay code is produced by circularly shifting the second Golaycode by the predetermined amount. All subsequent Golay codes are alsoproduced by employing the same circular shift. In another aspect,circular shifts between Golay codes may comprise different amounts.

In one aspect of the invention, a set of codes may be derived from thesame delay vector but with different seed vectors. This allows the samehardware to be used to generate the different Golay codes by simplyemploying different seed vectors. This can provide up to six sets ofGolay codes (or code pairs) generated from the same delay vector, butwith a programmable set of seed vectors. In this case, the seed vectormay be changed for each data symbol to be spread. Alternatively, a ReedSolomon code may be employed and the seed vector changed every 8symbols.

FIG. 3 illustrates a method for implementing wireless communications ina spatial multiplexing channel in accordance with one aspect of theinvention. In spatial multiplexing, multiple communication links areassigned to a common frequency channel. A Golay-code assignment step 301provides for assigning a unique set of Golay codes to each of aplurality of potentially interfering communication links. The assignmentstep 301 may comprise determining if interference is likely to occurbetween communication links. For example, the assignment step 301 may beconfigured to determine if two or more transceivers withomni-directional beam patterns are in close proximity. Alternatively,the assignment step 301 may be configured for detecting co-channelinterference between links, and if the interference exceeds apredetermined threshold, each link may be assigned a unique set of Golaycodes.

The assigned codes may comprise Golay codes stored in memory (i.e.,predetermined codes) or Golay codes generated on the fly. Generating thecodes may precede or follow the assignment step 301. In one aspect, theassigned codes are generated by each transceiver. For example, cyclicshifts of a Golay code may be employed for generating multiple spreadingcodes. Complementary Golay codes may be employed. In some aspects of theinvention, a plurality of seed vectors may be employed in a Golay-codegenerator having a fixed delay vector. Alternatively, a Golay-codegenerator may comprise multiple delay vectors. Any combination of thepreviously recited code-generation techniques may be employed in aspectsof the invention.

A spreading step 302 provides for spreading data with the selectedspreading codes. For example, each transceiver may be configured tospread 302 its data with its corresponding prescribed set of spreadingcodes. The spreading step 302 may be further configured to use the Golaycodes to randomly spread the data. For example, the spreading step 302may comprise changing the spreading code for each symbol or for each ofa predetermined set of symbols to produce a spread signal that istransmitted 303. This flattens the spectrum of the transmitted signal.At a Golay matched-filter receiver, spreading can randomize thelocations of autocorrelation sidelobes.

Golay code generation may be performed using a combination of delayelements, seed vector insertion elements, multiplexers, and/or one ormore combiners, such as described with respect to FIG. 5. Since Golaycode generation is an iterative process employing memory from previousiterations, matched filtering at a receiver may be performed with two ormore Golay matched filters such that adjacent symbols with differentcodes are handled by different matched filters. For example, if twofilters are employed, a first filter may process even-numbered symbols,and a second filter may process odd-numbered symbols.

FIG. 4 is a block diagram of an apparatus configured for communicatingin a millimeter-wave system. A means for assigning Golay codes to beused for spreading may include a Golay-code assignment module 401configured for selecting predetermined Golay codes stored in memory ordynamically generating Golay codes. The code-assignment module 401 maycomprise a computer-processing element and a memory wherein thecomputer-processing element is configured for selecting one or moreGolay codes stored in the memory. The computer-processing element may beconfigurable for performing calculations, such as determiningcross-correlation values or other relationships between candidate Golaycodes.

According to one aspect of the invention, the code-assignment module 401may select Golay codes having low cross-correlation for use in differentcommunication links. For example, the code-assignment module 401 mayselect one or more Golay codes for its communication link that have lowcross-correlation with Golay codes employed in another communicationlink used by a different system.

FIG. 5 is a block diagram of a Golay-code generator that may be employedin some aspects of the invention. The Golay-code generator comprises asequence of delay elements 501-509, a sequence of adaptable seed vectorinsertion elements 521-529, a first set of combiners 511-519, and asecond set of combiners 531-539 configured for combining delayed signalswith signals multiplied by the seed vector.

According to one aspect of the invention, the sequence of delay elements501-509 is configured for providing a predetermined set of fixed delaysD=[D(0), D(1), . . . , D(N−1)] to a first input signal. The sequence ofadaptable seed vector insertion elements 521-529 is configured formultiplying a second input signal by at least one of a plurality ofdifferent seed vectors W^(i)=[W^(i)(0), W^(i)(1), . . . , W^(i)(N−1)],i=1, . . . , L, where L is the number of Golay code pairs. The seedvector insertion elements 121-129 are programmable, and each seed vectorproduces a different Golay complementary code pair. The seed vectors mayinclude any combination of binary and complex symbols. For binary codes,W(k)=±1. For complex codes, W(k)=±1 and ±j. The delay profile (i.e., thedelay vector) provided by the delay elements 501-509 may be fixed, evenwhen the code generator is configured to produce multiple Golaycomplementary code pairs.

A means for spreading data with the Golay codes may include a spreadingmodule 402 configured for spreading each data symbol with the selectedGolay codes to produce a spread signal. The spreading module 402 isconfigured to employ the selected Golay codes in a way that randomlyspreads the data. For example, the spreading module 402 may comprise arandomizer (not shown) configured for randomizing the order in whichGolay codes are used to spread data.

According to one aspect of the invention, the spreading module 402 maycomprise a cyclic shifting module (not shown) for cyclically shiftingthe selected Golay codes before they are used to spread data. A cyclicshift of a Golay code comprises moving one or more elements from the endof a Golay code vector a=[a₀ a₁ . . . a_(N−1)] to the beginning of thevector. For example, a cyclic shift of one element of the Golay codevector a⁽⁰⁾=[a₀ a₁ . . . a_(N−1)] can be expressed as a⁽¹⁾=[a_(N−1) a₀a₁ . . . a_(N−2)]. Alternative aspects of the invention may employdifferent cyclic shifts.

A means for transmitting the spread signal may comprise a transmitter403 configured for up-converting, amplifying, and coupling the spreaddata signal into a wireless communication channel. The transmitter 403typically comprises a digital-to-analog converter, a frequencyup-converter, a power amplifier, and an antenna configured for couplingthe transmission into a wireless communication channel.

Various aspects described herein may be implemented as a method,apparatus, or article of manufacture using standard programming and/orengineering techniques. The term “article of manufacture” as used hereinis intended to encompass a computer program accessible from anycomputer-readable device, carrier, or media. For example, computerreadable media may include, but are not limited to, magnetic storagedevices, optical disks, digital versatile disk, smart cards, and flashmemory devices.

FIG. 6 illustrates software components residing on a computer-readablememory 600 and configured in accordance with an aspect of the invention.In this description, the term “memory” refers to data stores, algorithmstores, and other information stores. It will be appreciated that thememory components described herein can be either volatile memory ornonvolatile memory, or can include both volatile and nonvolatile memory.By way of illustration, and not limitation, nonvolatile memory caninclude read only memory (ROM), programmable ROM (PROM), electricallyprogrammable ROM (EPROM), electrically erasable ROM (EEPROM), or flashmemory. Volatile memory can include random access memory (RAM), whichacts as external cache memory. By way of illustration and notlimitation, RAM is available in many forms such as synchronous RAM(SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rateSDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM), anddirect Rambus RAM (DRRAM). Additionally, the disclosed memory componentsof systems and/or methods herein are intended to comprise, without beinglimited to, these and any other suitable types of memory.

A Golay code assignment source-code segment 601 is configured forassigning Golay codes to be used for spreading. According to one aspectof the invention, the source-code segment 601 is configured forselecting one or more Golay codes stored in memory. For example, thesource-code segment 601 may be configurable for determiningcross-correlation values between candidate Golay codes. According to oneaspect of the invention, the source-code segment 601 may select Golaycodes having low cross-correlation for use in different communicationlinks.

According to another aspect of the invention, the Golay code assignmentsource-code segment 601 may be configurable for providing apredetermined set of fixed delays D=[D(0), D(1), . . . , D(N−1)] to afirst input signal. The source-code segment 601 may also be configuredfor multiplying a second input signal by at least one of a plurality ofdifferent seed vectors W^(i)=[W^(i)(0), W^(i)(1), . . . , W^(i)(N−1)],i=1, . . . , L, where L is the number of Golay code pairs. The sourcecode segment 601 may be programmed with different seed vectors, whereineach seed vector produces a different Golay complementary code pair.

A spreading source code segment 602 is configured for spreading eachdata symbol with the selected Golay codes to produce a spread signal.For example, the source code segment 602 may randomize the order inwhich Golay codes are used to spread data. According to one aspect ofthe invention, the source code segment 602 may be configured forcyclically shifting the selected Golay codes before they are used tospread data.

Aspects of the invention may provide for beamforming in which a firstset of beacon signals is transmitted using a set of quasi-omni patterns,followed by transmitting a second set of beacon signals on apredetermined number of directional beam patterns. Such aspects mayprovide for different spreading gains for different beam patterns. Forexample, higher spreading gains may be selected for quasi-omni patternsthan for directional beacon patterns.

FIG. 7 is a flow diagram for a communication method in accordance withan aspect of the invention. A first beacon signal is constructed 701 andtransmitted 703 over a set of R quasi-omni beam patterns. The set of Rquasi-omni transmissions employs common-mode transmissions, whichtypically have the highest spreading gain of the available transmissionmodes. According to one aspect of the invention, transmitting the firstbeacon signal 703 comprises simultaneously transmitting the first beaconsignal over the set of R quasi-omni beam patterns. According to analternative aspect of the invention, transmitting the first beaconsignal 703 comprises sequentially transmitting the first beacon signalover the set of R quasi-omni beam patterns. For example, the firstbeacon signal is transmitted in R different directions, wherein eachdirection corresponds to one of the R quasi-omni beam patterns. Each ofthe R quasi-omni beam patterns is transmitted at a different time. Thus,the first beacon signal is transmitted once on each of the R quasi-omnibeam patterns and at different times.

The first beacon signal comprises a preamble, a header, and a dataportion. In accordance with one aspect of the invention, the preamblecomprises 32 repetitions of a length-128 Golay code, and the data isspread with one or more length-64 Golay codes. In other aspects of theinvention, Golay codes may have different lengths and/or differentnumbers of repetitions. The header or data portion of the first beaconmay include information about the second beacon signal. For example, thedirectional beacon information may include the Golay-set number s (wheres can be 0, 1, . . . S−1), the Golay code length used in the preamble,the number of repetitions used in the preamble, and the Golay codelength for header and data spreading.

A second beacon signal is constructed 702 and transmitted 704 over a setof directional beam patterns. A directional beam pattern may includedirectional beams generated from an antenna array or sector directionsgenerated by sector antennas. The second beacon signal may comprise aplurality of directional beacon signals. In accordance with one aspectof the invention, the directional beacon signals are transmitted 704simultaneously over the set of directional beam patterns. According toan alternative aspect, the directional beacon signals are transmitted704 sequentially over the set of directional beam patterns. For example,the directional beacon signals are transmitted in Q differentdirections, wherein each direction corresponds to one of Q directionalbeam patterns. Each directional beacon signal is transmitted once on oneof the Q directional beam patterns, and each transmission occurs at adifferent time.

The second beacon signal may use shorter Golay codes and fewerrepetitions in the preamble than the first beacon signal. For example,if the device transmitting the directional beacons has an antenna gainof 6 dB=10 log₁₀(4), it may use a length-64 Golay code during thepreamble that is repeated only 16 times, and the data may be spread withlength-16 Golay codes. This is equivalent to an overall spreading gainequal to one-fourth that of the common mode.

Constructing the first beacon signal 701 and constructing the secondbeacon signal 702 may comprise generating Golay code sets having a setof lengths (e.g., code lengths M=8, 16, 32, 64, 128, 256, and/or 512).Delay vectors and seed vectors may be selected for generating the codesets. For the above-recited code lengths, delay-vector and seed-vectorlengths would include N=3, 4, 5, 6, 7, 8, and 9. For each code length, aset of up to six code sets may be selected, such as described in U.S.patent application Ser. No. 11/599,725.

Each code-set comprises a fixed delay vector D=[D₀, D₁ . . . D_(N−1)] oflength N=log₂(M) and all the seed vectors W=[W₀, W₁ . . . W_(N−1)]. Thenumber of binary seed vectors (W_(k)=±1, k=0, 1, . . . , N−1) is 2N, andthe number of complex seed vectors (W_(k)=±1 or ±j, k=0, 1, . . . , N−1)is 4N. The binary seeds may be used for common-mode signaling in thequasi-omni beacons. The directional beacons may choose to implementcomplex seed vectors.

Constructing the first beacon signal 701 comprises selecting Golay codesets for use with the quasi-omni transmissions, and constructing thesecond beacon signal 702 comprises selecting Golay code sets for usewith the directional transmissions. The codes are selected such thattheir spreading gains compensate for the differences in antenna gainbetween the quasi-omni and directional beams. Code set selection alsocomprises selecting code sets for the preamble and data transmissionshaving the same spreading-gain criteria.

In one aspect, devices in a piconet may use the common mode forquasi-omni beacons. The common mode may include a length-128 code forthe preamble with 32 repetitions. This code may be generated using onebinary seed vector only (e.g., one fixed delay vector of length 7 andone fixed seed vector of length 7). For the directional beacon withantenna gain of 6 dB, the preamble code set is implemented using onebinary or complex seed vector and has length 64 (one fixed delay vectorof length 6 and one fixed seed vector of length 6) and 16 repetitions,which provides one-fourth of the spreading gain of the common-modepreamble. Alternatively, the directional beacon may employ a Golay codeof length 128 and provide for 8 repetitions, which also providesone-fourth of the spreading gain of the common-mode preamble.

FIG. 8 is a block diagram of an apparatus configured in accordance withan aspect of the invention. A means for transmitting a first beaconsignal via a set of quasi-omni beam patterns comprises a beam-patterngenerator 803 and a transmitter 804. A means for transmitting a secondbeacon signal via a set directional beam patterns also comprises thebeam-pattern generator 803 and the transmitter 804. In this case, thebeam-pattern generator 803 is configured for generating beam-formingweights for an antenna array that is part of the transmitter 804. Thebeam-forming weights comprise both quasi-omni beam pattern weights anddirectional beam pattern weights.

A beacon signal generator 802 employs Golay codes generated by a meansfor generating Golay codes, such as a Golay code generator 801, toproduce a first beacon signal for transmission on a plurality ofquasi-omni beam patterns. The beacon signal generator 802 also uses theGolay codes to produce a second beacon signal for transmission on aplurality of directional beam patterns. The beacon signal generator 802produces the first beacon signal such that its transmission rate ishigher than the transmission rate associated with the second beaconsignal. For example, the second beacon signal may use shorter Golaycodes and fewer repetitions in the preamble than the first beaconsignal.

FIG. 9 illustrates software components residing on a computer-readablememory 900 and configured in accordance with an aspect of the invention.A first beacon source code segment 901 is configured for constructing afirst beacon signal for transmission via a set of quasi-omni beampatterns. The first beacon signal is constructed from one or more Golaycodes to provide for a first transmission rate. A second beacon sourcecode segment 902 is configured for constructing a second beacon signalfor transmission via a set of directional beam patterns. The secondbeacon signal is constructed from one or more Golay codes to provide fora second transmission rate. The second beacon signal may use shorterGolay codes and fewer repetitions in the preamble than the first beaconsignal. Thus, the first transmission rate will be higher than the secondtransmission rate.

FIG. 10 is a flow diagram depicting a method for generating a preamblewith a set of extended Golay codes having low-cross-correlation. In oneaspect of the invention, a family of Golay codes may be extended byusing a Kronecker product of short sequences with Golay codes to obtaina larger set of Golay codes (i.e., extended Golay codes) with improvedcross-correlation properties. For example, an optional step ofgenerating extended Golay codes 1001 may comprise employing thefunctions kron([1 1 1 1], golay64) and kron([1-1 1-1], golay64) togenerate length-256 sequences of extended Golay codes having zeroperiodic cross-correlation.

In a related aspect, the Kronecker product of the following foursequences

$\quad\begin{bmatrix}1 & 1 & 1 & 1 \\1 & {- 1} & 1 & {- 1} \\1 & j & {- 1} & {- j} \\1 & {- j} & {- 1} & j\end{bmatrix}$

with the a Golay code of length 64 produces four sequences of length 256having zero periodic cross-correlations.

A code-set of length-64 (e.g., one fixed delay vector of length 6 andone or more binary seed vectors of length 6) may be selected for dataspreading in the quasi-omni case, whereas a length-16 code-set (onefixed delay vector of length 4 and multiple binary or complex seedvectors of length 4) may be used in the directional case. Alternatively,a code-set of length 16 (one fixed delay vector of length 4 and allbinary or complex seed vectors of length 4) may be employed for thequasi-omni case, and a code-set of length 8 (one fixed delay vector oflength 3 and all binary or complex seed vectors of length 3) may be usedin the directional case.

Extended Golay codes with zero cross-correlation may be selected 1002for different preambles, and one or more preambles may be generated 1003from the selected codes.

FIG. 11 is a block diagram of an apparatus configured for generating apreamble. A means for obtaining an extended Golay code may comprise anoptional Golay code selector 1101, an optional short-sequence selector1102, a Kronecker operator 1103, and an extended Golay code selector1104. The Golay code selector 1101 may be configured to generate one ormore Golay codes or select one or more Golay codes from a memory. Theshort-sequence selector 1102 may be configured to generate one or moreshort sequences or select one or more short sequences from a memory. Theshort sequences may comprise rows of a Fourier transform matrix or rowsof a Hadamard matrix.

The Kronecker operator 1103 is configurable for performing a Kroneckerproduct of the selected Golay codes with the selected short sequences toproduce a set of extended Golay codes having zero periodiccross-correlation. The extended Golay code selector 1104 is configuredto select an extended Golay code from the set of extended Golay codes toprovide a selected extended Golay code.

A means for generating a preamble may comprise a preamble generator 1105configurable for using the selected extended Golay code to generate thepreamble.

FIG. 12 illustrates software components residing on a computer-readablememory 1200 and configured in accordance with an aspect of theinvention. A Kronecker operator source code segment 1201 is configuredfor performing a Kronecker product operation of an input set of Golaycodes with an input set of short sequences to produce a set of extendedGolay codes having zero periodic cross-correlation. An extended Golaysource code segment 1202 is configured for selecting an extended Golaycode from the set of extended Golay codes to provide a selected extendedGolay code. A preamble generation source code segment 1203 isconfigurable for using the selected extended Golay code to generate apreamble.

In one aspect of the invention, the input set of Golay codes may begenerated by a Golay code generation source code segment (not shown)residing on the computer-readable memory 1200, and the input set ofshort sequences may be produced by a short sequence generation sourcecode segment (not shown) residing on the computer-readable memory 1200.The short sequence generation source code segment (not shown) may beconfigured to generate a Fourier transform matrix or a Hadamard matrix.

In yet another aspect of the invention, a method for generating acommunication signal for transmission shown in FIG. 13 comprisesgenerating a data block 1301 from input Golay codes and data portions,wherein every data portion of the data block is between two Golay codesand every Golay code is between two data portions, and transmitting thedata block 1302. A data payload is either generated dynamically orobtained from the MAC layer. The payload is scrambled, encoded, and thenpartitioned into data blocks. The data blocks are partitioned into dataportions, and Golay codes are inserted in between the data portions. Asub-block, as used herein, may comprise a data portion followed by aGolay code or a data portion preceded by a Golay code.

FIG. 15 shows a sub-block that comprises a cyclic prefix 1501 and asub-slot 1502. A sub-slot may comprise a Golay-code modulated datasequence. For example, the Golay-code modulated data sequence maycomprise {a₆₄d₀, a₆₄d₁, a₆₄d₂, a₆₄d₃} where d₀, d₁, d₂ and d₃ can bebinary, i.e. ±1, complex or multilevel. Thus, a sub-block comprises adata portion (i.e., a data sub-slot) and may further comprise at leastone of a cyclic prefix and a cyclic postfix. Assuming an FFT length of256 and a channel delay of 16 symbols, the last 16 symbols of the256-length sub-slot 1502 are typically copied and appended to the frontof the sub-slot 1502 as cyclic prefix 1501. This copy is necessary tomake the convolution cyclic, but it is not used in any other way.

FIG. 16 illustrates an alternative aspect of the invention in which thesub-slot length may be reduced by the channel delay. The term channeldelay, as used herein, is meant to include any evaluation of channeldelay, including, but not limited to, mean delay, maximum delay,root-mean-squared (rms) delay spread, average rms delay spread, and meandelay spread. For example, the sub-slot 1612.1 length may be 256-16=240symbols. A Golay sequence of length 16 is used as the prefix 161 1.1,and a postfix 1613 is appended to the last sub-slot 1612.N of thesequence of sub-slots. Thus, a sub-block may comprise a data portion(i.e., a sub-slot) preceded by a Golay sequence, a sub-block followed bya Golay sequence, or any combination thereof. In this aspect, the Golaysequence is the same for all sub-slots 1612.1-1612.N. In other aspects,the Golay sequences employed in cyclic prefixes may alternate betweensequence a and sequence b. In this case, the convolution is stillcyclic, so equalization in the frequency domain is still provided.However, the cyclic prefix 1611.1 and postfix 1613 can now be used totrack the channel and timing and frequency offsets using the Golayreceiver aspects of the invention. It is anticipated that this aspectmay be adapted to alternative FFT lengths, channel delay spreads, and/orGolay code lengths without departing from the scope of the invention.

FIG. 17 illustrates an aspect of the invention in which each of thefirst N/2 sub-slots 1722.1-1722.N/2 employs a first complementary Golaycode a as a prefix 1721.1-1721.N/2, respectively. Each of the next N/2sub-slots 1722.(N/2+1)-1722.N employs a second complementary Golay codeb as a prefix 1721.(N/2−1)-1721.N, respectively. Furthermore, sub-slot1722.N/2 employs a postfix 1723, and sub-slot 1722.N employs a postfix1724.

FIG. 18 illustrates a sub-block structure in accordance with an aspectof the invention configured to reduce the presence of spectral lines dueto periodic structure in the frame. Since the prefix occurs at regularintervals, if the same prefix is used in each interval, the transmissionhas at least one strong spectral line in the frequency domain. Aspectsof the invention may employ a different prefix for each of a pluralityof sub-slots in order to reduce or eliminate spectral lines resultingfrom the periodic structure in the frame. For example, a cyclic prefixgenerator may be configured to cyclically shift the Golay code used inthe cyclic prefix 1831.1-1831.3 for each sub-slot by a predeterminednumber of chips C. FIG. 18 shows the case where the Golay code iscyclically shifted by C=1 chip for each successive sub-slot. The datasub-slot length including the Golay-code length is 256+1, since only thelast 15 chips of the prefix is cyclic with the first 15 chips of thefollowing postfix.

Each sub-slot may comprise a single-carrier or an OFDM signal. However,the sub-slot length may differ for each mode. Furthermore, sub-slotlength may vary, such as with respect to channel conditions, or variousalternative parameters.

In one aspect of the invention, the sub-slot length is set to a multipleof the parallel processing factor of the receiver (e.g., 4). In thiscase, the sub-slot length may be 244 while the Golay code is still oflength 16. The cyclic shift is selected to be C=4, such that thecyclic-prefix length is 16−C=12 and the FFT length 256 is performed overeach sub-slot and the 12 repeated chips of the Golay code.

FIG. 19 illustrates a sub-block structure that may be employed invarious aspects of the invention. A unified single-carrier and OFDMsub-block structure is provided wherein each sub-slot contains asingle-carrier signal or an OFDM data portion, and the sub-slot lengthcorresponds to an FFT length. Each sub-slot may have time-domain and/orfrequency-domain pilot symbols, such as may be used for timing andfrequency tracking. Time-domain pilot symbols are typically used in thesingle-carrier case and known frequency-domain pilots are employed withOFDM transmissions. The pilots may be scrambled in time or frequency tominimize spectral lines.

A known Golay code {a₀, a₁, . . . , a_(L−1)} of length L (e.g., L=16) isinserted before each sub-slot, and it may be used for timing, frequency,and channel tracking. Furthermore, the Golay code may be cyclicallyshifted as previously described to mitigate spectral lines. Some aspectsof the invention are configured to transmit data having the structureshown in FIG. 19. However, the received signal x_(0:N−1) correspondingto a sub-slot is not a cyclic convolution between the data and thechannel impulse response.

The received signal corresponding to the Golay code after sub-slot 1 isdenoted as y_(0:L−1). We form the following vector z_(0:N−1), where

z _(k) =x _(k) +y _(k) for k=0, . . . , L−1 and z _(k) =x _(k) for k=L,. . . , N−1.

The constructed signal z_(0:N−1) has two components z⁽¹⁾ and z⁽²⁾, where

z _(n) ⁽¹⁾ =u _(n)

h _(n) n=0, 1, . . . , N−1

is the cyclic convolution of length N between the channel and thetransmitted data in the sub-slot, sub-slot data is denoted u₀, u₁, . . ., u_(N−1), and

z _(n) ⁽²⁾ =a _(n)

h _(n) n=0, 1, . . . , L−1

is the cyclic convolution of length L between the channel and the knownGolay code. This latter part affects only the first L samples ofz_(0:N−1).

In order to make the convolution cyclic, z_(n) ⁽²⁾ n=0, 1, . . . , L−1can be computed since the Golay code is already known and the channel isestimated at the receiver, then subtracted from the first L samples fromz. The resulting vector is z_(n) ⁽¹⁾ n=0, 1, . . . , N−1, which is acyclic convolution. Those skilled in the art will note that there aremany known fast algorithms to compute the cyclic convolution z_(n)⁽²⁾=a_(n)

h_(n) n=0, 1, . . . , L−1. The cyclic convolution allows OFDMequalization and single-carrier equalization, including frequency-domainequalization.

FIG. 20 illustrates another aspect of the invention in whichcomplementary Golay code a is inserted before even numbered sub-slots,complementary Golay code b is inserted before odd numbered sub-slots,and known pilot chips or tones are inserted in some or all of thesub-slots. The use of complementary Golay codes in this manner providesseveral benefits. For example, improved channel tracking may be achievedbecause the sum of the autocorrelations of the two sequence a and b is aDirac function in the time-domain, and therefore has no sidelobes. Thetime-domain Dirac function is flat in the frequency domain, thus it doesnot produce spectral lines.

The term x_(0:N−1) is denoted as the received vector corresponding to asub-slot, and y_(0:L−1) is the vector corresponding to the Golay codefollowing the sub-slot. The vector z_(0:N−1) has the following threecomponents:

z _(n) ⁽¹⁾ =u _(n)

h _(n) n=0, 1, . . . , N−1,

which is the cyclic convolution of length N between the channel and thetransmitted data in the sub-slot,

${z_{n}^{(2)} = {{{\left( \frac{a_{n} + b_{n}}{2} \right) \otimes h_{n}}\mspace{14mu} n} = 0}},1,\ldots \mspace{14mu},{L - 1},$

which is the cyclic convolution of length L between the channel and theaverage of the two Golay code, and

${\begin{bmatrix}z_{0}^{(3)} \\z_{1}^{(3)} \\\vdots \\z_{15}^{(3)}\end{bmatrix} = {\begin{bmatrix}h_{0} & {- h_{1}} & \ldots & {- h_{L - 1}} \\h_{1} & h_{0} & \ldots & {- h_{L - 2}} \\\vdots & \vdots & \ddots & \vdots \\h_{L - 1} & h_{L - 2} & \ldots & h_{0}\end{bmatrix}\begin{bmatrix}{\left( {a_{0} - b_{0}} \right)/2} \\{\left( {a_{1} - b_{1}} \right)/2} \\\vdots \\{\left( {a_{L - 1} - b_{L - 1}} \right)/2}\end{bmatrix}}},$

which is the pseudo-cyclic convolution of length L between the channeland the difference of the two Golay codes. The matrix ispseudo-circulant.

In order to make the convolution cyclic, the second term z_(n) ⁽²⁾ n=0,1, . . . , L−1, and third term, z_(n) ⁽³⁾ n=0, 1, . . . , L−1 can becomputed and subtracted from the first L terms of z. The second andthird terms involve known quantities, so they can be computed easily.Those skilled in the art will appreciate the availability of fastalgorithms that compute cyclic and pseudo-cyclic convolutions.

The resulting value is z_(n) ⁽¹⁾=u_(n)

h_(n) n=0, 1, . . . , N−1, which is a cyclic convolution between theunknown data and the estimated channel. Conventional OFDM equalizationis now possible, as well as any of the various single-carrierequalization schemes, including frequency domain equalization.

In one aspect, an apparatus is configured for generating a sub-slottransmission sequence with a cyclic prefix and a cyclic postfix. In thecase wherein the apparatus employs a Fourier transform of length N, aGolay sequence generator is configured for generating a Golay sequencecomprising M symbols, wherein M<N. A sub-slot sequence generatorproduces a Golay-code modulated data sequence having a sub-slot lengthof N−M symbols, and a cyclic prefix generator employs the Golay sequenceto produce the cyclic prefix (and a cyclic postfix), wherein each of thecyclic prefix and the cyclic postfix comprises M symbols. At least oneof the cyclic prefix generator and the Golay sequence generator isconfigured to change the Golay used in the cyclic prefix. For example,the Golay code may be cyclically shifted for each cyclic prefix.Alternatively, different Golay codes may be used such that the codechanges for each successive cyclic prefix.

FIG. 14 is a block diagram of an apparatus configured for generating asignal in accordance with an aspect of the invention. A means forgenerating a first data block comprising Golay codes and data portionsmay include a data block generator 1401 configured for receiving theGolay codes and data. The data block generator 1401 is configured forgenerating data blocks wherein every data portion is between two Golaycodes and every Golay code is between two data portions. A means fortransmitting the data block may comprise a transmitter 1402 configuredto up-convert, amplify, and couple the data block into a wirelesscommunication channel.

In one aspect of the invention, the Golay codes employed in the dataportion are identical. In another aspect, the Golay codes comprisecyclic shifts of a seed Golay code. In another aspect, the Golay codescomprise complementary Golay codes. A sub-block may comprise one of theGolay codes and one of the data portions, or a portion of a first one ofthe Golay codes followed by one of the data portions followed by aportion of a second one of the Golay codes. Each sub-block may comprisea number of chips that is a power of two or a power of two plus one. Insome aspects, the data portion may have a length that is power of two.

In one aspect of the invention, a first one of the Golay codes functionsas a cyclic prefix of a sub-block comprising one of the data portionsfollowed by a second one of the Golay codes. The sub-blocks may bedemodulated by using cyclic prefix and cyclic postfix portions of theGolay codes. In another aspect, a first one of the Golay codes functionsas a cyclic postfix of a sub-block comprising a second one of the Golaycodes followed by one of the data portions. The Golay-code length may beconfigurable with respect to various parameters. For example, theGolay-code length may be a function of multipath delay.

The apparatus shown in FIG. 14 may be configured to generate a firstdata block employing a first set of Golay codes, and a second data blockusing Golay codes that are different from the Golay codes used togenerate the first data block.

The invention is not intended to be limited to the preferred aspects.Furthermore, those skilled in the art should recognize that the methodand apparatus aspects described herein may be implemented in a varietyof ways, including implementations in hardware, software, firmware, orvarious combinations thereof. Examples of such hardware may includeASICs, Field Programmable Gate Arrays, general-purpose processors, DSPs,and/or other circuitry. Software and/or firmware implementations of theinvention may be implemented via any combination of programminglanguages, including Java, C, C++, Matlab™, Verilog, VHDL, and/orprocessor specific machine and assembly languages.

Those of skill would further appreciate that the various illustrativelogical blocks, modules, processors, means, circuits, and algorithmsteps described in connection with the aspects disclosed herein may beimplemented as electronic hardware (e.g., a digital implementation, ananalog implementation, or a combination of the two, which may bedesigned using source coding or some other technique), various forms ofprogram or design code incorporating instructions (which may be referredto herein, for convenience, as “software” or a “software module”), orcombinations of both. To clearly illustrate this interchangeability ofhardware and software, various illustrative components, blocks, modules,circuits, and steps have been described above generally in terms oftheir functionality. Whether such functionality is implemented ashardware or software depends upon the particular application and designconstraints imposed on the overall system. Skilled artisans mayimplement the described functionality in varying ways for eachparticular application, but such implementation decisions should not beinterpreted as causing a departure from the scope of the presentdisclosure.

The various illustrative logical blocks, modules, and circuits describedin connection with the aspects disclosed herein may be implementedwithin or performed by an integrated circuit (“IC”), an access terminal,or an access point. The IC may comprise a general purpose processor, adigital signal processor (DSP), an application specific integratedcircuit (ASIC), a field programmable gate array (FPGA) or otherprogrammable logic device, discrete gate or transistor logic, discretehardware components, electrical components, optical components,mechanical components, or any combination thereof designed to performthe functions described herein, and may execute codes or instructionsthat reside within the IC, outside of the IC, or both. A general purposeprocessor may be a microprocessor, but in the alternative, the processormay be any conventional processor, controller, microcontroller, or statemachine. A processor may also be implemented as a combination ofcomputing devices, e.g., a combination of a DSP and a microprocessor, aplurality of microprocessors, one or more microprocessors in conjunctionwith a DSP core, or any other such configuration.

The method and system aspects described herein merely illustrateparticular aspects of the invention. It should be appreciated that thoseskilled in the art will be able to devise various arrangements, which,although not explicitly described or shown herein, embody the principlesof the invention and are included within its scope. Furthermore, allexamples and conditional language recited herein are intended to be onlyfor pedagogical purposes to aid the reader in understanding theprinciples of the invention. This disclosure and its associatedreferences are to be construed as being without limitation to suchspecifically recited examples and conditions. Moreover, all statementsherein reciting principles, aspects, and aspects of the invention, aswell as specific examples thereof, are intended to encompass bothstructural and functional equivalents thereof. Additionally, it isintended that such equivalents include both currently known equivalentsas well as equivalents developed in the future, i.e., any elementsdeveloped that perform the same function, regardless of structure.

It should be appreciated by those skilled in the art that the blockdiagrams herein represent conceptual views of illustrative circuitry,algorithms, and functional steps embodying principles of the invention.Similarly, it should be appreciated that any flow charts, flow diagrams,signal diagrams, system diagrams, codes, and the like represent variousprocesses that may be substantially represented in computer-readablemedium and so executed by a computer or processor, whether or not suchcomputer or processor is explicitly shown.

1. A method of communication, comprising: transmitting a first beaconsignal via a set of quasi-omni beam patterns; and transmitting a secondbeacon signal via a set directional beam patterns, wherein a first rateassociated with the transmission of the first beacon signal is higherthan a second rate associated with the transmission of the second beaconsignal.
 2. The method recited in claim 1, wherein the first beaconsignal is transmitted at different times.
 3. The method recited in claim1, wherein the second beacon signal is transmitted at different times.4. The method recited in claim 1, wherein the first rate is a functionof Golay code length and number of Golay code repetitions used in apreamble of the first beacon signal, and the second rate is a functionof Golay code length and number of Golay code repetitions used in apreamble of the second beacon signal.
 5. The method recited in claim 1,wherein information about signal structure associated with the secondbeacon is transmitted in the first beacon.
 6. An apparatus forcommunication comprising: means for transmitting a first beacon signalvia a set of quasi-omni beam patterns; and means for transmitting asecond beacon signal via a set directional beam patterns, wherein afirst rate associated with the transmission of the first beacon signalis higher than a second rate associated with the transmission of thesecond beacon signal.
 7. The apparatus recited in claim 6, wherein thefirst beacon signal is transmitted at different times.
 8. The apparatusrecited in claim 6, wherein the second beacon signal is transmitted atdifferent times.
 9. The apparatus recited in claim 6, wherein the firstrate is a function of Golay code length and number of Golay coderepetitions used in a preamble of the first beacon signal, and thesecond rate is a function of Golay code length and number of Golay coderepetitions used in a preamble of the second beacon signal.
 10. Theapparatus recited in claim 6, wherein information about signal structureassociated with the second beacon is transmitted in the first beacon.11. A machine-readable medium comprising instructions encoded thereonand executable to: transmit a first beacon signal via a set ofquasi-omni beam patterns; and transmit a second beacon signal via a setdirectional beam patterns, wherein a first rate associated with thetransmission of the first beacon signal is higher than a second rateassociated with the transmission of the second beacon signal.
 12. Anapparatus for communication, comprising: a first module configured totransmit a first beacon signal via a set of quasi-omni beam patterns;and a second module configured to transmit a second beacon signal via aset directional beam patterns, wherein a first rate associated with thetransmission of the first beacon signal is higher than a second rateassociated with the transmission of the second beacon signal.